# Distributional Gaussian Processes Layers for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2206.13346 · HTML: https://mlsanity.com/paper/2206.13346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 94 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 30 of 58)

- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images](https://mlsanity.com/paper/1804.04488/) (2018)
- [Exploring Uncertainty Measures in Deep Networks for Multiple Sclerosis Lesion Detection and Segmentation](https://mlsanity.com/paper/1808.01200/) (2018)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [PHiSeg: Capturing Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/1906.04045/) (2019)
- [Robust Large Margin Deep Neural Networks](https://mlsanity.com/paper/1605.08254/) (2016)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)

## Built on by (most cited first, 1 of 1)

- [General OOD Detection via Model-aware and Subspace-aware Variable Priority](https://mlsanity.com/paper/2512.13003/) (2025)

## Abstract (arXiv)

Machine learning models deployed on medical imaging tasks must be equipped with out-of-distribution detection capabilities in order to avoid erroneous predictions. It is unsure whether out-of-distribution detection models reliant on deep neural networks are suitable for detecting domain shifts in medical imaging. Gaussian Processes can reliably separate in-distribution data points from out-of-distribution data points via their mathematical construction. Hence, we propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving Gaussian Processes with a distance-preserving affine operator on distributions. Our experiments on brain tissue-segmentation show that the resulting architecture approaches the performance of well-established deterministic segmentation algorithms (U-Net), which has not been achieved with previous hierarchical Gaussian Processes. Moreover, by applying the same segmentation model to out-of-distribution data (i.e., images with pathology such as brain tumors), we show that our uncertainty estimates result in out-of-distribution detection that outperforms the capabilities of previous Bayesian networks and reconstruction-based approaches that learn normative distributions. To facilitate future work our code is publicly available.